A Novel Approach to Spectral MRI
Tiffany A. Fetzner

List of Symbols

Symbol  Definition 
g  gyromagnetic ratio for hydrogen 42.58 MHz / Tesla
d chemical shift
q angle of projection
Sij Summation of all pixels in an image
BW  bandwidth
BWT  bandwidth theoretical
CH2 methylene hydrogen, A chemically characteristic peak in fat
CH3 methyline hydrogen, A chemically characteristic peak in fat
CSA chemical shift artifact
EPR electron paramagnetic resonance
FOV  field of view 
Fs Maximum quadrature sampling rate
FT  Fourier transform 
G gradient
Hz hertz unit of frequency cycles/second
i row index for chemical shift components
I1 Original Test Image
I2 theoretical RT
I3 theoretical IRT reconstruction
I4 theoretical reconstruction compared to original =I4= total square difference image
I5 experimental RT
I6 experimental IRT reconstruction
I7 experimental reconstruction compared to original =I7=  total square difference image
I8 comparison of difference image I4 to difference image I7 = difference image I8
IRT inverse Radon transform 
j column index for chemical shift components
MHz mega-hertz unit of frequency  106cycles/second
MR magnetic resonance
MRI magnetic resonance imaging
MRS magnetic resonance spectroscopy
n interger numbers from 1 up to 256
N Scale factor of 65,536
NMR nuclear magnetic resonance 
r spin density
pixel picture element
PSA Projection Slice Algorithm
P(y,q,d) projection of spatial coordinate y with respect to q and d. 
RT Radon transform 
S(TR,TE) signal with respect to TR and TE
S-S  spatial-spectral 
S-S-S spatial-spatial-spectral 
S-SI  spatial-spectral  imaging 
S-S-SI  spatial-spatial-spectral  imaging
T1 spin-lattice relaxation time
T2 spin-spin relaxation time
TE echo-time
TR repetition time
VBW  variable-bandwidth 
voxel volume element
x spatial coordinate x
y spatial coordinate y
Table of Contents | Thesis